An Investigation of the Application of the Rayleigh-Ritz Method to the Deflection of a Small Aspect Ratio Swept Plate of Uniform Thickness

Citation

Wechsler, Joseph Wolff (1950) An Investigation of the Application of the Rayleigh-Ritz Method to the Deflection of a Small Aspect Ratio Swept Plate of Uniform Thickness. Engineer's thesis, California Institute of Technology. doi:10.7907/JSWQ-0P95. https://resolver.caltech.edu/CaltechETD:etd-03132009-153457

Abstract

An investigation was initiated to examine the possibility of improving the rate of convergence of a series solution for the deflection of a swept cantilever plate of uniform thickness, using the Rayleigh-Ritz method, by applying the solution to low aspect ratio plates instead of high aspect ratio plates as had been done previously. The Rayleigh-Ritz deflection functions which were used were products of vibration modes of uniform clamped-free and free-free bars.

Deflections were computed, using six terms in the series, for three different loading conditions at sweep angles of 20°, 40°, and 60°. The results, plotted against experimental data in Figures 7 to 24, show that the rate of convergence is satisfactory only for angles of sweep of 20° or less. Since the cases of sweep of 20° or more are of most interest in the application to swept back aircraft wings, it was concluded that the rate of convergence is not satisfactory.

The possibility of improving the rate of convergence of the series solution by solving for the difference between the true deflections and the deflections given by some approximate formula was indicated as the next step in arriving at a satisfactory solution. It was pointed out that the experimental data mentioned above would provide a valuable guide in the formulation of such an approximate formula.

Thesis Files